# Tagged Questions

Questions involving philosophy of mathematics. Please consider if Philosophy Stack Exchange is a better site to post your question.

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### How do we know logic works? [duplicate]

Every time I read about a theory in mathematics, it usually starts with axiomatizing the most fundamental concepts that are going to be treated. Recently, I have started finding this troubling. In ...
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### Are theorems like subroutines for math? [on hold]

I've been developing more appetite for math just lately, as I study electromagnetics to deepen my understanding of electric circuits and devices. I'm finding that doing derivations as exercises helps ...
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### Infinite sums vs infinite unions

Why is it that For every set $S$, there exists a set $\bigcup S$. is something we take for granted (even though $S$ could be infinite), while For every sequence $a_1,a_2,\dots$ of numbers, ...
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### Basic atoms in mathematics [closed]

Given the concepts '1', 'set' and 'sum' (and maybe 'point' for geometry), can you build the whole mathematics upon then? If not, what other basic atoms would you need?
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### Is math an exact science? [closed]

The day before yesterday I talked with a friend of mine about math. He is also a PhD student like me, and in his opinion math cannot be consider an exact science, because the same statement could be ...
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### Is it possible to be a frequentist and a subjectivist at the same time?

I'm trying to understand the differences between (1) Bayesian vs frequentist; and (2) subjectivist vs objectivist. So far my understanding (correct me if I'm wrong) is that: (1) Bayesian vs ...
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### Differences between constructivism and formalism

What are the main differences between the formalism and constructivism in mathematics? Is there some theorem or axiom valid in formalism which isn't valid in constructivism and vice versa? Is the ...
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### In “10 grams of salt”, is the unit “grams”?

The gram is a unit of mass, so "10 grams" has "grams" as the unit. "10 pounds" uses a different unit. So what is the "salt" in "10 grams of salt", if not a unit? In other words, what is the ...
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### Any “exotic” foundations of mathematics? [closed]

There is a myriad of axiomatizations of set theory (a branch of mathematics obviously not at all identical with notorious ZFC) and other formal systems working with classes, categories and such. All ...
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### Why does $p$ (is true) strictly agree with $p$ while $p$ (is false) strictly disagrees?

Let's make the truth table: $$\begin{array}{|c|c|c|} \hline p&(p) \text{ is true}&(p) \text{ is false}\\ \hline T&T&F\\ F&F&T\\\hline \end{array}$$ "$p$ is true" strictly ...
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### Logical explanation why exponentiation operation is not commutative and associative

Considering Peano axioms we'll define addition, multiplication and exponentiation operations. We can then prove that addition and multiplication operations are commutative and associative. The proof ...
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### Scalar multiplication as a special form of matrix multiplication

Question What do we gain or lose, conceptually, if we consider scalar multiplication as a special form of matrix multiplication? Background The question bothers me since I have been reading about ...
56 views

### Impossibility of proving a foundation to be consistent

An argument came to my mind that seems really mind-blowing and I haven't found it anywhere. Here's how it goes: We call a formal system F embodied in classical logic a foundation of mathematics when ...
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### Quasi mathematical objects [closed]

I was looking on this post http://www.songho.ca/math/euler/euler.html and I came to the comment that says "i is not a number at all. It is an ill-formed concept. There is a vast difference between a ...
39 views

### Could relational operators be used to construct formal theory of natural numbers which is “stronger” than Peano Axioms?

This is a beginner's question about foundational construction of (alternative?) number theory. The notion of mathematical equality is closely related to logico-philosophical notion of 'Law of Identity'...
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### Does defining a type of mathematical object require defining a binary relation of “equality”?

I'm trying to determine whether defining a type of mathematical object requires us to know what we mean by another object being "equal" to it. For example, when we define a type of object like set, ...
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### Developments from Charles Peirce's logic diagrams?

These last weeks I have been revisiting Charles Sanders Peirce's logical or thought diagrams (what he called, alpha, beta and gamma diagramms) and I found many of them highly interesting. Some ...
168 views

### What exactly are the numbers we use everyday?

Pi can be defined as diameter / circunference of a circle. But what is a circle? You can't tell a computer: "build a circle and divide its diameter by its ...